Steps

Get a dual-wieldable weapon. The easiest one to get is the smg, because you often spawn with it. There should be many more around the map though.

2

Find a second weapon. Using the secondary weapon controls, hold Y for the XBOX and The XBOX 360 but for the PC Hold Q. You should now have both weapons in your hands.

3

Now that you have two weapons you are currently dual wielding.

4

To fire your weapons hit both the right trigger and the left trigger at the same time. Or for the PC use the left click for the left weapon and the right click for the right.

5

Experiment with multiple weapon combinations. An SMG and a Plasma Rifle's different damage styles but fast rate of fire wear through shields faster than two SMGs or two Plasma Rifles. Also, a Plasma Pistol and any other weapon is effective for neutralizing enemy shields with a charged shot.